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Mexico City is actually built on the floor of what used to be Lake Texcoco. The lake was quite prominent back when the city was called Tenochtitlan. Manmade drainage systems largely removed the shallow lake which wasn't especially potable in the first place.

I think Canberra counts. It does have a decent sized lake, Lake Burley Griffin, in the middle of it but that's artificial in the sense that they took an existing river and put a dam in it to make a lake.

What is a "World capital"? I'm sure there are some national capitals without access to waterways/bodies of a water above a certain size. The ability to answer this question really depends on your definitions.

One possible example is the city of Riyadh, capital of Saudi Arabia, that has import water via pipline. Wiki Link